Performance Improvement of Coded OFDM Communication … · Performance Improvement of Coded OFDM...

International Journal of Computer Applications (0975 – 8887)

Volume 110 – No. 11, January 2015

17

Performance Improvement of Coded OFDM

Communication System in AWGN Channel

Marwa Abdelfatah Abdeltwab Instructor, Dept. of EECT,

Modern Academy in Ma'adi, Egypt

K.A. ElBarbary Professor and Head of Electric Engineering Department, Suez

Canal University, Egypt

Adel Elhenawy Professor, Dept. of Electrical Communication, Ain Shams

University, Egypt

ABSTRACT

OFDM (orthogonal Frequency Division Multiplexing) is a

basic element in the 4G mobile system. The OFDM

performance can be improved using the channel coding. The

channel coding is a class of signal transformations designed to

improve communication system performance.

The work presented in this paper discusses the performance

improvement of OFDM communication system using

different channel coding techniques through AWGN channel

model. These coding techniques include Reed Solomon

coding, Convolutional coding, Concatenated coding (by

combining Reed Solomon with Convolutional), and

Interleaved concatenated coding techniques. Besides, a new

algorithm produced to choose a good convolutional encoder

design for a certain rate and memory registers.

Keywords

OFDM, AWGN, Channel Coding, Reed Solomon,

Convolutional, Interleaver.

1. INTRODUCTION In recent years Orthogonal Frequency Division Multiplexing

(OFDM) has gained a lot of interest in digital communication

application. This has been due to its important features like

robustness to multipath fading channel and high spectral

efficiency [1, 2, 3]. OFDM is used in many digital

applications as digital audio broadcasting (DAB), digital

video broadcasting (DVB), Wireless Local Area Networks

(WLAN), and other high speed data application for both

wireless and wired communications [1,3].

OFDM overcomes most of the problems with older multi-

channel systems that use FDMA and TDMA. OFDM splits

the available bandwidth into many narrow band channels. The

carriers for each channel are made orthogonal to each other,

allowing them to be spaced very close together, with no

overhead in guard spacing between bands as in the FDMA

technique, and there is no great need for users to be time

multiplex as in TDMA, so that there is no overhead associated

with switching between users. As each band is narrow, the

symbol rate is low that limits the problem of multipath delay

spread [4].

The channel coding is used to improve the performance of un-

coded OFDM systems. There are many types of coding

technique that used in OFDM as block code and convolutional

code [5]. The concatenated code is a coding technique that

uses two or more different codes to provide a large coding

gain with less implementation complexity [6]. The interleaved

concatenated code is the concatenated code with the use of an

interleaver between the two coding techniques to achieve

better improvement in the system performance [7].

The rest of the paper organized as follow:

Section 2 shows the concept of OFDM system. Section 3

shows the concept of different types of channel coding

techniques that can be used in OFDM, including Reed

Solomon, Convolutional, Concatenated, and interleaved

concatenated codes. Section 4 shows the BER performance of

uncoded and coded QPSK-OFDM over AWGN channel.

The simulation results presented in this paper demonstrate the

advantage of systems with error control coding over uncoded

system performances in terms of the coding gain.Finally

Section 5 concludes the paper.

2. OFDM CONCEPT Orthogonal Frequency Division Multiplexing (OFDM) is a

communication technique that divides the available bandwidth

into a number of equally spaced frequency bands. Each band

has a subcarrier that carries a portion of the user information.

Each subcarrier is orthogonal to each other, allowing

overlapping between the bands without interference between

them, and also cause saving of bandwidth as referred in Fig 1

[1, 8, 9].

Fig 1: Saving Bandwidth using OFDM

Each carrier in an OFDM signal has a very narrow bandwidth;

so that the resulting symbol rate is low (symbol time is large).

This will give the signal a high tolerance to Multipath delay

spread, because the delay spread must be very long to cause

significant inter-symbol interference, and in order to totally

eliminate ISI, OFDM employs a cyclic prefix which increases

the length of the symbol period so that it is much greater than

the delay spread of the channel [3, 4].

Fig 2 below shows the block diagram of an OFDM system

[10].

Fig 2: OFDM General Block Diagram



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The input data is first passed to the forward error correction

(FEC) encoder to improve the system performance by adding

redundant bits to the data. The coded signal is then sent to the

modulator where the bits are mapped to symbols, which is

represented in in-phase and quadrature (IQ) format.

The IFFT is then used for modulating the constellation

mapped data onto the orthogonal subcarriers. The IFFT

generally takes N symbols at a time where N represents the

number of subcarriers in the system. Since the basis functions

for an IFFT are N orthogonal sinusoids, all subcarriers will be

orthogonal [10]. S/P and P/S converters used to adjust the

format of the data depending on the input of the next block.

Finally a cyclic extension is added, and transmits through the

channel.

3. CHANNEL CODING Channel coding is the transformation of the signal in a certain

designed method to enable the transmitted signals to better

withstand the effects of various channel impairments such as

noise, interference and fading [5].

3.1 Reed Solomon Code Reed Solomon (RS) codes are nonbinary cyclic codes with

symbols made up of m-bits sequences. The most conventional

RS code with (n, k) = (2m-1, 2m-1-2t) with dmin= n-k+1 [5].

Where k: number of data symbols, n: number of code

symbols, m: number of bits in each symbol.

The RS encoder take k data symbols and add 2t redundant

symbols to produce n code symbols where each symbols

contain m bits [11]. The RS decoder has 2t redundant symbols

which are twice the amount of correctable errors t, as for each

error, one redundant symbol is used to locate the error and

another redundant symbol is used to find its correct value [5].

The RS encoding process for the message word m(x),

involves the following steps:

1. Generate the generating polynomial:

G(x) = g0+g1x+g2x2+……+g2t-1x

2t-1+x2t

2. Generate the parity polynomial:

P(x) = xn-km(x) modulo G(x)

3. The required codeword polynomial will be:

U(x) = P(x) + xn-km(x) [5]

RS codes are designed to deal with the burst errors. As RS is a

nonbinary code, it works with symbol based arithmetic rather

than bit based arithmetic so that it can be configured with long

block length (in bits) and large dmin with less decoding time,

but this increase the complexity [5].

Shortening is performed to improve the performance of the

RS code. It done by fixing the rate (k/n) and reduce both the

message length (k) and the codeword length (n), so it have the

same redundancy and the same error correcting capability as

the original code but with less complexity, less decoding time

and sometimes less power consumption. It is implemented by

appending a certain number of zeros to the information

message at the input of the original encoder then discarded

these added zeros after the coding procedure [12].

3.2 Convolutional Code A general convolutional encoder consists of k shift registers

and n modulo-2 adders as shown in Fig 3 [5].

Fig 3: Convolutional Encoder

The message bits are shifted into the encoder one bit at a time,

and the outputs of the n adders are sequentially sampled and

transmitted, so that there are n code bits for each message bit

and the code rate is 1/n [5] . So, the output sequence is

function of both the current input bit and the k-1 previous bits

[13]. The convolutional decoder uses the viterbi algorithm

that is optimal as it performs maximum likelihood decoding.

It reduces the computational load by taking the advantage of

the special structure of the code trellis. As the trellis diagram

represents the rules of the game as it describes all possible

transitions and their corresponding state and finish states, so

the error path must follow one of the allowable transitions. So,

there are constraints in the encoding process, which cause the

decoder to more easily meet good error performance using

less Eb/No [5].

The choice of connection between the adders and the registers

in convolutional encoder provides a certain characteristics to

the code. These connections are not chosen arbitrary, it must

be chosen to yield good distance properties of the code, and it

found by computer search for all possible connection to find

the best. [5]

.The puncturing technique is used to improve the

performance of a convolutional code, it obtained by

puncturing or eliminating some outputs of the convolutional

encoder. This technique increases the rate of the code and

reduces the decoding complexity and time, but it reduces the

distance of the code so reduce the error correcting capability

of the code. [14]

3.3 Concatenated Code A concatenated code is a very useful technique that leads to

construct a powerful code that can provide large coding gain

with less implementation complexity [10]. A big, powerful

code with high BER performance can be constructed in an

equivalent concatenated form by combining two or more

codes of relatively small size and complexity to provide the

same performance with less complexity, and decoding is done

by combining two or more relatively low complexity decoders

instead of a complex decoding of a big code [7].

3.4 Serial Concatenated Code In a serial concatenated code, a message block is first encoded

by the first code, normally called the outer code, then the

output from the first code encoded by the second code,

usually called the inner code. The decoding process operates

in two stages: first performing the decoding of the inner code

and then the decoding of the outer code. The decoding

complexity decomposed into these two decoders is much

lower than that of the direct decoding of the whole code as

shown in Fig 4 [7, 15].

The concatenation between two codes will yield a new code

with the following parameters:

The length = n1*n2

The minimum distance <= dmin1*dmin2



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The rate = R1*R2 [7, 15]

Where: the inner code has length n1, minimum distance dmin1,

and rate R1, and the outer code has length n2, minimum

distance dmin2, and rate R2.

Fig 4: Serial Concatenated Code

3.5 Interleaved Concatenated Code Interleaving is a technique that takes a given sequence of

symbols and permutes their positions and arranging them in a

different temporal order. Interleavers are used against burst

errors, so it is designed to convert error patterns that contain

long sequences of serial erroneous data into a more random

error pattern, so distribute errors among many code vectors,

Burst errors are characteristic of some channels, like the

wireless channel, and they also occur in concatenated codes,

where an inner decoder overloaded with errors can pass a

burst of errors to the outer decoder [7]. Fig 5 represents

interleaved concatenated code.

Fig 5: Interleaved Concatenated Code

4. THE PERFORMANCE OF OFDM

SYSTEM IN AWGN CHANNEL This section includes the BER performance of uncoded and

coded OFDM over AWGN channel.

The OFDM system parameters used according to IEEE Std

802.16.1a-2013. The modulation technique is QPSK, FFT

length equals 1024 and the cyclic prefix (CP) length equals

1/8 of the symbol length [16]. The performance of the system

is determined by the relation between bit error rate (BER) and

bit energy to noise ratio (Eb/No). Assume that, the desired

quality of transmission is BER = 10-4 and the objective is to

achieve this BER with the minimum power as possible.

4.1 The BER Performance of uncoded

OFDM The BER performance of the uncoded OFDM system over the

AWGN channel can be represented theoretically by

theoretical BER for QPSK equation:

BER=0.5*erfc ( Eb/No) [10]

And also can be represented practically by simulation as

shown in Fig 6.

Fig 6: Theoretical and Practical Uncoded OFDM

From Fig.6, the desired BER which is 10-4 achieved in the

uncoded OFDM at Eb/No = 8.2 dB. So the target is to achieve

the same quality of transmission but at lower power level.

4.2 Uncoded OFDM versus coded OFDM This section discusses the performance improvement for

OFDM system using different channel coding techniques.

4.2.1 Reed Solomon coded OFDM

4.2.1.1 The Performance of RS Codes Depends on

the Redundancy and the Codeword Length This section shows the performance of Reed Solomon code

through AWGN channel model, by changing the codeword

length and keeping the code rate with the optimum value

which assumed to be 0.7 as mentioned in reference [5].

Fig 7: Reed Solomon coded OFDM with Different Lengths

According to Fig 7, the RS coded system performance

improved with increasing its codeword length. So the best

performance achieved with RS (255,179) which achieve the

desired BER at Eb/No = 5.5 dB, so achieve approximately 2.7

dB as coding gain. Coding gain refers to the saving in Eb/No

due to the used coding technique.

4.2.1.2 Shortened RS Coded OFDM From Fig 8, the shortened RS code, which have

approximately the same rate as the original code, will result

approximately the same bit error performance, it provides the

desired BER at the same power level that as the original code,

besides reducing the complexity and decoding time.



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Fig 8: Shortened RS Coded OFDM

4.2.2 Convolutional coded OFDM In the simulation of OFDM using convolutional coding

technique, there are two an extra points must be discussed:

4.2.2.1 A New Method to Input the Data to the

Convolutional Encoder In the normal way, the input data enters to the convolutional

encoder, then at the decoder, There exist a trace back delay

which is a delay that the decoder need to create the complete

view about the trellis diagram that used in the decoding

process, and after this trace back delay, the decoder begin to

output the decoded data. So, due to this delay the decoded

data contains number of zero bits at the first, which equal to

the trace back length in bits, followed by the decoded data that

refers to the original data, but with missing of the last number

of bits in the original data. So the decoded data will be the

original data with missing of some bits.

For example with convolutional code with 1/n=1/2 and K=3

and generator polynomial [7, 5] with a trace back delay =3:

msg_entered_to_encoder =

1 0 1 1 1 0

encoded_msg =

1 1 1 0 0 0 0 1 1 0 0 1

decoded_msg =

0 0 0 1 0 1

In the new method, the input to the encoder will be the input

data followed by number of zero bits equal to the trace back

delay length. So that, at the decoder with certain trace back

length, after the trace back delay the decoded data will contain

firstly number of zero bits equal to delay length, followed by

the decoded data that refer to the original data without any

missing in the original data but ignoring the last bits in the

data which is the previously added zero bits. So that, with this

new method, the whole original data will appear in the

decoded data without missing. For the same previous

example, by adding 3 zero bits to the data that enter to the

encoder:

msg_entered_to_encoder =

1 0 1 1 1 0 0 0 0

encoded_msg =

1 1 1 0 0 0 0 1 1 0 0 1 1 1 0

0 0 0

decoded_msg =

0 0 0 1 0 1 1 1 0

In the simulation, because of the number of transmitted bits

will be very large, the normal way with ignoring the last bits

of the data and the new method without ignoring data will

provide approximately the same results in the calculation of

BER performance. But, the new method will be mainly

important in the practical case.

Also it is useful in the concatenated code, where the output of

the inner decoder (convolutional) will be entered as input to

the outer decoder (Reed Solomon), in the case of using the

normal way the output of convolutional decoder, with

ignoring the last bits of the data, must be appended with zero

bits before entering to the outer decoder (RS), so the decoder

also recover the original data with missing of some bits.

But, when using the new method in the concatenated code, the

output of the convolutional decoder includes the whole

original data, so this output enters directly to RS decoder.

This new method does not affect the system rate, and this is

because the very large number of transmitted data with

respect to the number of added zero bits. Also it provides a

little difference in the BER performance in a certain range of

SNR due to the same previous reason as shown in Fig 9. But

mainly this method will affect in the practical system.

Fig 9: Convolutional Coded OFDM with New Method

The original data without any missing in the data bits

The zero bits due to the trace

back delay

The added zero bits

The original data with missing of the last 3 bits

The zero bits due to the trace

back delay back delay



21

4.2.2.2 A new algorithm to Create a Good

Convolutional Code This algorithm can be used to select the best connection for

the convolutional encoder to achieve the large distance that

represents a measure to the error correcting capability of the

code.

This algorithm start its work by selecting the required rate 1/n

and constraint length K, then testing the all possible

connection of the encoder to find the best connection that has

a large free distance. From the matlab simulation of this

algorithm, to create a good convolutional code, by selecting

rate = 1/n = 1/2 and constraint length = K=3, the

convolutional encoder design with maximum free distance

will have the best connection as shows:

good_conv_code =

'n' 'k' 'max dfree' 'best connection vector'

[2] [3] [5] [5 7]

[2] [3] [5] [7 5]

So, there are many choices of the encoder circuit connections

that have a maximum distance. Fig 10 shows the flowchart

that illustrates the simulation process of choosing the good

distance convolutional encoder design.

Fig 10: An Algorithm to Select Convolutional Code with Large Distance

4.2.2.3 The Performance of Convolutional Codes

with Different Parameters Here, the convolutional coded system is simulated for

different rates and different constraint lengths (K). From Fig

11, the convolutional code with large constraint length and

large rate provides a better performance, but the preferred rate

for convolutional code is 1/2 as it will limit some of

bandwidth consumption.

The convolutional coded system with rate 1/2 and K 7 will

achieve the target BER at 5.5 dB.

Fig 10: Convolutional coded OFDM



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4.2.2.4 Punctured Convolutional Coded System

Performance Fig 12 examines the performance of the punctured

convolutional code with different rates. It appears that, for the

punctured convolutional code with rate 2/3, the rate increases

but the performance degrades. For the other curves, as the rate

approximately remain constant its error correcting capability

still fixed and its performance as the case of the original

convolutional code, and its benefit is to save some decoding

time and complexity by saving or removing only a small

number of bits that out from the encoder. So, the punctured

convolutional code adjusted to make a balance between its

advantage and disadvantage, to have the same performance

with less complexity. Finally, this technique can be adjusted

according to the application requirements.

Fig 11: Punctured Convolutional Coded System

4.2.3 Concatenated coded OFDM Firstly, the Reed Solomon code concatenated with the

convolutional code. The concatenation is done between two

moderate codes the first is RS code, with lower redundancy so

more simple, and the second is the convolutional code with

rate 1/2, which use Viterbi algorithm that makes it also simple

in computation. Fig 13 shows that, the code that uses RS

(255,239) and the other that use RS (255,195) provides the

desired BER at 3dB and 3.1 dB respectively, with coding gain

approximately equal 5.2 dB than the uncoded case.

Fig 12: Concatenated Coded OFDM

4.2.4 Concatenated Coded System with Less

Decoding Complexity and Time The system performance can be enhanced by using the

shortened version of RS (255,239) which is RS (204,188) and

the punctured version of convolutional code with rate 1/2

which is punctured convolutional with rate 50/97, as shown in

Fig 14.

Fig 13: Concatenated Coded OFDM Using the Shortened

RS and the Punctured Convolutional Codes

From the previous figure, the modified concatenated coded

OFDM system, with shortened RS and punctured

convolutional, provides approximately the same performance

as that the normal concatenated code but with less complexity

and decoding time.

4.2.5 Interleaved Concatenated coded OFDM The use of interleaver in the concatenated system will

improve the error performance. Fig 15 shows that the

performance for Interleaved Concatenated code OFDM

system, the interleaved concatenated coded OFDM system

will achieve the desired BER at 2.6 dB. Which means that

there is a coding gain = 5.4 dB with Interleaved Concatenated

OFDM system than the uncoded case.

Fig 14: Interleaved Concatenated Coded OFDM

Finally, Fig 16 shows the performance of uncoded versus

different types of coded OFDM system, and the used coding

technique depends on the available resources and the

application requirement.



23

Fig 15: Uncoded OFDM versus coded OFDM

As shown in the previous figures, the different coding

techniques improve the performance of OFDM system by

reaching lower BER at earlier Eb/N0. But there is a crossover

between uncoded and coded performance, which means that

, at low values of Eb/N0 , the uncoded system has a lower BER

than coded system.

The reason of this crossover is that every code system has

some fixed error correcting capability, and if the errors within

a block exceed code correcting capability, the code system

cannot correct it and perform poorly. Coding techniques,

which means adding redundancy, cause high data rate, less

energy per bit, and more errors out of the demodulator that

can reach and exceed code correcting capability, so cause

poor performance. So the benefits of coding in performance

appear at reasonable values of Eb/N0 that compensate the poor

performance of the demodulator. Using a powerful coding

techniques ,as concatenated codes, cause the crossover occur

at earlier point or provide improved performance at lower

values of Eb/N0 .[5]

5. CONCLUSION This paper presented the performance of uncoded versus

coded OFDM system over AWGN channel. That discusses

the effect of different channel coding techniques in the

performance of OFDM system. It shows the performance of

RS and convolutional codes in OFDM system, then discusses

the concatenation between them to provide a better

performance at earlier power level. It also discusses the ability

of interleaved concatenated codes to provide a more

improvement in the system. and its ability to use the shortened

and punctured techniques to respond to various systems

demands so provide the better performance with the available

resources with less decoding complexity and time. It also

introduced a new algorithm to choose a good convolutional

encoder design with certain rate and memory registers.

As a feature work, the concatenated codes will be applied in

the Rayleigh fading channel. And also, his effect on the PAPR

will be tested.

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[4] Teddy Purnamirza, The Performance of OFDM in

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IJCATM : www.ijcaonline.org

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